How to distinguish AI modeling from implementation?
One good way of differentiating modelling and implementation is to consider that models occupy a much higher level of abstraction. 

To continue with the mathematical example: even though experimental mathematics might be dependent on computation, the program can be considered as one possible realization of the necessary conditions of a more abstract existence proof.

Over the last 25 years, software engineering methodologies have become quite good at separating models and implementations, e.g. by using interfaces/typeclasses/abstract base classes to define constraints on behavior that is concretely realized by the implementation of derived classes.

AI has always been a battle between the 'neats and the scruffies'. Neats tend to prefer working 'top down' from clean abstractions, 'scruffies' like to work 'bottom up', and 'bang the bits' of the implementation together, to see what happens.

Of course, in practice, interplay between both styles is necessary, but AI as a science progresses when we abstract mechanisms away from specific implementations into their most general (and hence re-useable) form.